Summary: Controlling neural clustering
using delayed inputs
G´abor Orosz and Jeff Moehlis
Department of Mechanical Engineering, University of California,
Santa Barbara, California, 93106, USA
(e-mail: gabor@engineering.ucsb.edu, moehlis@engineering.ucsb.edu)
Abstract: Coupled Hodgkin-Huxley neurons are considered when finite-speed signal prop-
agation introduces time delays into the coupling. Bifurcations of the fully synchronous and
partially synchronized cluster states are studied by varying the coupling delay. Based on these
investigations a controller is constructed that uses delayed inputs to destroy full synchrony and
stabilize clustering. A generalization of such a controller may be useful to drive neural systems
away from pathological synchronous states associated with Parkinson's disease. Copyright
c IFAC 2009
Keywords: Hodgkin-Huxley model, signal transmission delay, bifurcation, event-based
act-and-wait control
1. INTRODUCTION
Neural systems have been studied mathematically for more
than half a century and they are well characterized at the
component level; see Hodgkin and Huxley (1952). Still,
their emergent rhythmic behavior is not fully understood.